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Tuesday, November 29, 2016

Collisions Problems with Solutions One

Collision is a physical action between two bodies where they exchange momentum and kinetic energy. There is no rule that the bodies need to come into contact for this to happen. Even with out physical contact, if the bodies of the system exchange their momentum and kinetic energy. For example an alfa particle striking towards a heavy nucleus, they deviate from their path and it also shall be treated as collision . If both linear momentum and kinetic energy are conserved, the collision is said to be elastic collision. If only linear momentum is only conserved and some of the kinetic energy is converted into light, heat or sound, that kind of collision is called inelastic collision.

Problem

A stationary shell explodes into two fragments with masses having ratio 1 : 2. If the kinetic energy of the heavier piece is 100 joule, we need to measure the kinetic energy released in the explosion.

Solution

As the body is initially in the state of rest, its initial linear momentum is zero.As momentum is conserved, by applying it we can get the ratio of velocities of the bodies as shown in the diagram below. With knowledge about both velocity and mass, we can find individual and total kinetic energy of the body as shown in the diagram below.

Solution

A uranium nucleus at rest emits an alpha particle with a velocity known. We need to find the recoil velocity of the remaining particle. Problem is as shown in the diagram below.

Solution

As there is no external force on the atom, linear momentum is conserved. As we know the mass of two parts, we can apply conservation of linear momentum and solve the problem as shown in the diagram below.

Problem

A particle of mass 3m is moving with a velocity and it has elastic collision with another particle of mass 2m which is at rest. We need to measure the final velocities of the bodies after collision. Problem is as shown in the diagram below.

Solution

We shall know the formulas to find the final velocities of the two bodies after one dimensional elastic collision and they are as mentioned below. Problem is further solved as shown.

Problem

A moving particle of mass m makes a straight collision with another particle of mass 4m which is at rest. We need to know the fraction of the kinetic energy retained by the incident particle and the problem is as shown in the diagram below.

Solution

As the collision is one dimensional elastic collision, coefficient of restitution is equal to one. So the ratio of velocity of separation after the collision is equal to the velocity of approach before the collision. Also by applying conservation of momentum, we can get one more equation and by simplifying them , we can solve the problem as shown in the diagram below.

Problem

A gun of mass M fires a bullet of mass m with a kinetic energy E. We need to measure the velocity of recoil of the gun.

Solution

By applying law of conservation of linear momentum, we can find the velocity of the second body as shown below. By substituting in the formula of kinetic energy, we can solve the problem as shown here.